Quantum computers process information according to the laws of quantum mechanics. This means an increase in computational processing for specific problems (i.e. function inversion with Grover's algorithm, and factoring large numbers into prime factors with Shor's algorithm).
Blockchain offers an open, public, distributed ledger that has many applications, including digital currencies. The security of this ledger depends on the difficulty of solving certain cryptographic problems which are threatened by the potential of quantum computation. Specifically, hashes as used in signing the blocks of the ledger can be compromised.
The principal threat is Grover's algorithm, which can dramatically speed up function inversion. This allows the generation of a modified pre-image from a given hash (a hash collision) allowing a signed data block to be modified. This destroys authenticity of the ledger entries undermining the entire blockchain.
The second threat is Shor's algorithm, which applies to any part of blockchain that relies on asymmetric key cryptography. The main problem is that of breaking RSA encryption. RSA relies on the ease of multiplying prime numbers in contrast to the difficulty of factoring large numbers into prime factors. Shor's algorithm speeds-up this process exponentially, effectively breaking RSA encryption. Variants of Shor's algorithm do the same for other asymmetric key cryptosystems.
To counter these threats few quantum-resistant cryptographic tools have been developed. Currently, the National Institute of Standards and Technology is responsible for navigating this threat. Congress has tasked NIST with R&D in cryptographic standards and tools to counter the threat of quantum computation. No standards are developed yet. Therefore, a quantum version of Blockchain is needed that is resistant to Quantum attacks.